Exceed ExpectationsAlexander Darishchev,* Pierre Lemouzy and

Patrick Rouvroy, Beicip-Franlab, France, outline some of the practical aspects of modelling

and flow simulation in the context of tight and shale gas reservoirs.

Unconventional hydrocarbon resources such as tight and shale gas play a significant role in overall production: over 50% of current US natural gas production and about 15%

of global natural gas comes from tight and shale gas reservoirs with estimated potential to rise over time.1 This gas occurs in extremely low permeability reservoirs. Recent advances in horizontal drilling and multistage hydraulic fracturing (Figure 1), and a better understanding of reservoir flow and production mechanisms have made the so-called ‘unconventional’ gas recoverable in the current high-price climate. Successful reservoir management requires close collaboration between different specialists with emphasis on multidisciplinary approaches not only in a technical context, but also in economic, legal and environmental areas. The focus of this study is on reservoir engineering. This is a challenging time to reconsider some of the issues around modelling and flow simulation in the context of tight and shale gas reservoirs and to exceed common expectations.

Simulation of flow in tight and shale gas reservoirsReservoir data collection and management is of central importance. Planning, justification, priority, timeliness, quality, cost-effectiveness and the robustness of technologies applied are the guiding factors that should now be reconsidered. Earth scientists, engineers and software developers have made considerable progress in the integration of both geoscience and engineering data: geological, geophysical, geomechanical and reservoir production data can be processed together via a platform of 3D modelling workflow and

integrated simulation software packages and modules. This enables geoscientists and engineers to handle a huge range of reservoir data and consider different scenarios in order to find the most plausible strategies for recovery optimisation and material and financial resource allocation. The gateway to successful business development in tight and shale gas is through smarter technologies, a new commitment to R&D and, of course, closer collaboration between different specialists with emphasis on multidisciplinary approaches and a collaborative environment. The marginal economics of unconventional reservoirs require more improvements in field data acquisition, reservoir characterisation, modelling and simulation abilities. Technological effectiveness and economic success are extremely sensitive to an overall ability to achieve expected gas production from such low permeability reservoirs. Another important issue is the ability to describe the reservoir in terms of performance, quantify the effectiveness of stimulation treatments and to forecast production and provide economists with curve plots, risk and uncertainty analysis tools. Production profiles are the key ‘input’ data for investment studies, revenue estimation and economic performance evaluation. Without the recognition of the critical elements, contributing components, geological features, physical and chemical phenomena, which occur in porous media, the application of production profiles and forecasts is questionable and cannot be properly used in decision-making.

The reservoirs of tight and shale gas tend to have lower permeability and higher heterogeneity, the parameters that govern fluid flow are numerous and uncertain. The focal limiting factors, key roadmap components, natural gas composition and shale and tight

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rock properties have been summarised before.2 Complex physics and non-linear hydrodynamic behaviour of flow make it difficult to forecast production and evaluate associated risk and uncertainties by applying existing analytical approaches that are based on solutions on the diffusion equation and assume the following: Ì The reservoir is homogeneous (constant porosity and

permeability), with a uniform thickness.

Ì Fluid flow is uniform over the entire thickness of the pay section (radial or linear).

Ì Single phase flow, constant viscosity of the flowing phase.

Ì Gravitational forces are neglected.

The main incentives for using a numerical reservoir simulator are the ability to model high heterogeneity reservoirs, the multiphase flow of complex fluids, different driving forces and interference between production and injection wells. The ability to handle complex geological models, and most particularly, to forecast production by considering different scenarios of development and thus make better business decisions ahead of time is the main objective and advantage of numerical simulations versus analytical approaches.

Due to significant changes in shale and tight gas well productivity and reservoir performance in the same localised areas in a seemingly random manner, the decision was made to use the OpenFlow SuiteTM platform, which is designed to integrate available field data, perform reservoir characterisation, modelling and numerical simulation, and to speed up the decision making process. This software also enables the accurate prediction of in situ reserves and simulates production profiles. Consisting of a complete suite of plug-in modules, the portfolio of this software enhances both synergy and communication between flexible workflows, and also honours the high quality requirements of the industry and R&D. A further part of this software, PumaFlowTM Reservoir Simulator, is based on rigorous physical formulations and provides high performance computing, user-oriented interface and work environment. The associated fracture modelling software FracaFlowTM assisted history matching and uncertainty management, whilst CougarFlowTM allowed the reservoir engineer to make reliable production forecasts for highly heterogeneous reservoirs and to better understand the impact of different parameters and associated uncertainties.

Some points concerning flow mechanisms and transport inherent in tight and shale gas reservoirs could be highlighted as follows: Ì Tight gas occurs in sands and carbonates, shale gas occurs

in organic-rich formations, and source rock as well as reservoirs. Three types of gas stored in shale formations can be distinguished: ‘free gas’ in natural fractures and pores, ‘adsorbed gas’ and ‘gas dissolved in kerogen and bitumen.’ The amount of adsorbed gas in shales varies from 15% (Barnett Shale, USA) to a maximum of 60 - 85% of original gas in place (OGIP) (Lewis Shale, USA). The contribution of the adsorbed gas to production can have a significant impact during the last phase of field exploitation, when the reservoir pressure is less than the characteristic adsorption pressure. The ability to produce the absorbed gas is limited because of the ultra-tight matrix rock, relatively high bottom hole pressure (BHP), and the desorption profile, which requires very low reservoir pressures to liberate the adsorbed gas. Due to different adsorption properties of natural gas components, the composition of gas produced can vary significantly during the desorption phase of gas production. Generally, field isotopic data show that the relative compositional decline of heavier molecular species of the gas is greater than that of lighter ones.

Figure 1. A horizontal well with hydraulic fractured stages (multi-stage fracturing).**

Figure 2. A quarter section of a fractured stage: SRV is represented by a simplified discrete fracture network with spatially variable permeability, unSRV (red).

Figure 3. Quarter sector model of a fractured stage. Vertical scale reduced by two. Variable SRV represented by a simplified fracture network (f-SRV) and matrix medium (m-SRV), unSRV contains only matrix medium (m-unSRV).

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Ì Fluid-flow regimes can be differentiated by the Knudsen number (a non-dimensional parameter defined as the ratio of the mean free path of gas molecules to the characteristic size of porous medium). The following regimes can be distinguished: continuum fluid flow (0 – 10-3), slip (10-3 – 10-1), transition (10-1 – 101), free-molecular (>101). Even if the characteristic size of pores is relatively very small: e.g. from 3 to 45 nm (Barnett Shale), the regime of gas flow can be considered as a continuum fluid flow. Nevertheless, the phenomenon of slip cannot be neglected in specific reservoir conditions. If laboratory measurements of permeability are performed under reservoir conditions, the Klinkenberg effect will be of second-order.

Ì The consideration of non-Darcy flow increases the complexity of a model that already has high uncertainties, even for the key parameters such as matrix and fracture porosities and permeabilities, stimulated reservoir volume (SRV), etc. The Darcy flow assumption can be applied as the first approach.

Hydraulic fracturing design aimed at the creation of effective fracture networks is a widely used technique for intensive stimulation of oil and gas wells, especially in cases of extremely low permeability formations, particularly tight and shale gas reservoirs (Figure 1). It includes up to 40 stages of fracturing and the SRV typically vary3 from 700x106 (P90)† – 2500x106 (P10) ft3/well, up to 4500x106 ft3/well). The network of propped hydraulic fractures provides the crucial flow paths from the shale matrix to the horizontal wellbore. Besides the hydraulically induced fractures, naturally occurring fractures and fissures contribute to reservoir flow as additional microflow paths and increase matrix-fracture exchange.

Adjustment of gridblock size and simulation time stepAs has been previously summarised,2 different authors have advocated the break-up of the hypothesis of the continuous reservoir: the drainage area, and the availability of reserves in unconventional reservoirs with extremely low permeability are based on a single well or even a single fractured stage consideration. One of the most difficult parameters to evaluate in tight and shale gas reservoirs is the size and shape of the drainage area. Months or even years of production are required for conventional well tests. As a result of increasing hardware efficiency and advancements in numerical methods, reservoir simulation is moving towards finer-grid models of reservoir and becoming an indispensable tool. However, despite the recent developments in computational speed techniques, it is not feasible to simulate reservoir flow behaviour with an ultrafine geological ‘statistically and physically realistic’ scale. A sector model scheme with explicit fracture network is, therefore, required in cases of extremely low permeability. The complexity of the physics and the magnitude of governing parameters and related uncertainties in fractured reservoirs can also be introduced with ‘classical’ methods: ‘dual porosity – single permeability’ and ‘dual porosity – dual permeability’ (known as ‘2Φ-1K’ and ‘2Φ-2K’ respectively), which allow flow simulations to speed up whilst providing satisfactory results.

Due to the long transition period in low and extremely low permeability reservoirs, applicability of the ‘pseudosteady-state’ assumption is questionable, particularly for the initial reservoir simulation as long as the pressure perturbation has not reached several gridblocks in the vicinity of the well. Several approaches were adapted to improve the run time of reservoir flow simulation, but these lack the ability to model transient behaviour. One of the most rigorous methods for modelling such reservoirs with induced hydraulic fractures is to use a logarithmically refined grid, including

a network of fractures, matrix blocks, stimulated and unstimulated domains, which have significant impact in terms of reservoir performance and recovery. As stated above, it has been assumed that the phenomenon of slip has a second order effect at high reservoir pressure, and the Darcy flow assumption has been applied.4

Ì P – Pressure.

Ì i – Axis index.

Ì xi – Coordinates (x1, x2, x3 for x, y, z).

Ì ki – Directional permeability.

Ì μ – Fluid viscosity.

Ì ρ – Fluid density.

Ì g – Gravity.

Ì z – Elevation.

Ì φ – Porosity.

Ì ct – Total rock and fluid compressibility.

Ì q – Sink term.

The selection of simulation time steps requires careful consideration of different limitations due to the assumptions made and numerical methods used. As referenced,5 the following limitations should be considered in reservoir flow simulation: stability (control of oscillations, calculation of relative permeability and capillary pressure), control of overshoot (that occurs most frequently with the gas phase) and control of truncation error (limitation of maximum pressure and saturation changes due to discrete approximations).

The maximum gridblock size to be used is also limited by ‘pseudosteady’ state assumptions; well block storage effects can be erased considering a fine reservoir grid. Decreasing the mesh size leads to better capture early time phenomena, such as well-block storage and propagation of pressure perturbation. In fact, due to very low permeability, the maximum gridblock size is limited by transient flow appearance and well-block storage effects. As has been mentioned before,4 when Td > 2.6 the derivative is flat, as expected by the analytical solution of the fluid flow equation. This time was determined as the one from which the apparent well-block storage effect ends, it leads to the following inequality:

Ì t – time.

Ì ∆L – characteristic gridblock size.

The maximum size of a gridblock should be adjusted a few feet with simulation time step (according to the inequality stated above2), in order to avoid apparent well-block storage effects, particularly, in the case of low and extremely low permeability.

A study on the simulation of flow in an extremely low permeability reservoirIn the study presented below, the reservoir properties have been selected according to reference field data with high spatial and temporal variability and uncertainties. Deterministic approaches

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geometry of fractured blocks of 10 ft x 28 ft x 180 ft, fracture and matrix permeabilities and KrPc properties have been retained from the reference model previously described. The in situ volumes of fluids have been adjusted via ‘fracture’ and ‘matrix’ porosities which refer, in these cases, to the whole fractured sector, not to a discrete fracture network and matrix medium, as in the reference case. The formation parameters were initialised as before: reference depth (7090 ft/2160 m), pressure (3800 psi/262 bar) and temperature (180 ˚F/82 ˚C).

Assuming symmetry of the drainage area and no interference between gas wells and fractured stages (in the case of an extremely low permeability reservoir) a quarter section of a fractured stage has been considered. It allowed the grid to be logarithmically refined and to explicitly represent a hydraulic fracture network, which is the major contributor in terms of flow. A refined quarter section is penetrated by a 5 in. horizontal well, the following SRV stage volumes have been considered (Figure 3): Ì 1. 50 ft x 335 ft x 180 ft (x4) = 12.1x106 ft3

Ì 2. 50 ft x 450 ft x 180 ft (x4) = 16.2x106 ft3

Ì 3. 50 ft x 675 ft x 180 ft (x4) = 24.3x106 ft3

Using field references and analytical data2 (Figure 4, Table 1), geomodelling software and the PumaFlow reservoir simulator, a sensitivity study of the dimension of SRV, matrix and propped fracture permeability, which are spatially varied (Figure 3), and of the bottom hole pressure as a technological parameter of exploitation, was performed. Assuming a pseudosteady state flow, the simulation time step and the gridblock size were adjusted. As observed in the field and laboratory practice, the fracture aperture and effective permeability depend on the distance between the wellbore and gridblocks modelled, and so this approach has also been applied (Figure 3).

The simulations of flow that were performed for a reference quarter sector to study pressure field in matrix and fracture media (Figures 5 and 6). They showed that the contribution of the unstimulated reservoir volume (in the vicinity of the SRV, where there are no hydraulically induced fractures) to the gas production is non-negligible. Rather, it can be a significant part of gas production and should be taken into account: up to 50%, depending on the geometry and shape of the SRV, the fracture and matrix permeabilities and porosities, and on the technological parameters of well exploitation, such as the flow rate and bottom hole pressure.2 No dewatering period has been considered; the gas flow rate was constrained for the early stages in order to have physical and consistent simulation results. The reservoir flow simulations were performed with the assumption of a negligible amount of adsorbed gas, which has no significant impact during the first

phase of production and pressure depletion. Nevertheless, multicomponent gas desorption can be taken into account by performing additional studies.

The comparison between the reservoir simulation results for the reference quarter sector model and the ‘2Φ-1K’, ‘2Φ-2K’ models – with the identical matrix medium and hydraulic fracture network properties, in situ volume of fluids, and fluid PVT – shows overestimation and underestimation of gas production for the considered period: about 5 – 13% (Figure 6). The ‘classical’ dual medium approach appears to provide satisfactory results with a significant gain in computation time (10 min versus 80 min in terms of CPU processing time). This enables decision-making to be sped up and provides reasonable approximations and forecasts for scenario and uncertainty analyses.

therefore have not been used. Five key reservoir parameters are thought to affect gas recovery: the porosity and permeability of both matrix and fracture media, as well as SRV. The purpose of this reservoir simulation study was to provide a representative reservoir model capable of capturing different phenomena inherent in extremely low permeability reservoirs (such as tight and shale gas) and obtain plausible and reliable production profiles.

A reservoir model based on field data has been considered as a method of evaluating the impact of hydraulic fracturing SRV, matrix and propped fracture permeability, which were spatially varied, as one of the most realistic approaches, and the bottom hole pressure, as a technological parameter of exploitation. Due to the long transient period, simulation of such gas reservoirs requires careful consideration of the simulation time step and gridblock size: an adjustment is required (pseudosteady state assumption). A quarter section of a fractured stage (100 ft x 900 ft x 180 ft) has been discretised and the grid has been logarithmically refined (737 100 gridblocks), the fracture network was represented by fine gridblocks, this allows the three main regions to be regionalised and thus distinguished: ‘0’ – matrix medium of unstimulated reservoir volume (m-unSRV), ‘1’ – matrix medium of stimulated reservoir volume (m-SRV) and ‘2’ – fracture medium of stimulated reservoir volume (f-SRV), (Figure 2). This allows fracture and matrix media to be represented independently and to ‘populate’ the grid with spatially varied properties: rock type, porosity, permeability, relative permeability, capillary pressure curves (KrPc) and end-points, compressibility, phase saturation, PVT data, etc. This approach enables integration of different data (e.g. porosity and permeability distribution in the fractures according to microseismic imaging, saturation of fluids, etc.) and to treat them as history matching parameters. Due to the complexity of the reference model with an explicit fracture network and relatively long CPU simulation time, two simplified equivalent reservoir models have also been studied via the ‘classical’ dual medium approaches: ‘dual porosity – single permeability’ and ‘dual porosity – dual permeability’ (2Φ-1K and 2Φ-2K respectively) to speed up flow simulations. The simplified

Figure 4. Relative permeability curves: fracture medium (left), matrix medium (right), two different rock-types, analytical formulae and empirical data used.

Table 1. Selected parameters for sensitivity study

Parameter Variables

No. Description Min Mode Max Unit

1 SRV per stage 12.1 16.2 24.3 106 ft3

2 Matrix permeability 10 100 1000 nD

3Propped fracture permeability

1 2 10 D

4 Min BHP 500 1000 1500 psi

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Conclusions Ì The properties of matrix and fracture media (geometry,

interconnectedness, porosity, permeability) have a significant impact on producibility: when the flow capacity of a fracture network is reached, additional production from the unSRV (in the vicinity of the SRV) due to pressure decline and exchange surface can present a non-negligible amount of gas to be taken into account. Matrix properties play a key role in recovery. Fracture networks enhance flow capacity.

Ì The reference sector model represented by a logarithmically refined grid with a simplified network of discrete fractures has allowed for a better understanding of flow behaviour and the production mechanism in an extremely low permeability reservoir.

Ì Integration of spatially distributed fractures and of their properties, particularly porosity and permeability, seems to be one of the most realistic approaches (e.g. fracture permeability can be spatially variable depending on the distance between the wellbore and the gridblocks to model). In comparison with previous studies, it has been stated that the proposed approach of modelling can be used in cases where the dual medium approach is questionable or inappropriate.

Ì The comparison between the reference sector model and 2Φ-2K and 2Φ-1K models – with the identical matrix medium and hydraulic fracture network properties (size of fracture blocks, permeabilities, etc.), in situ volume of fluids, and PVT – shows overestimation and underestimation of gas production for the considered period: between 5 and 13%. These models provide satisfactory results with a significant gain in computation time (10 min versus 80 min in terms of CPU processing time).

Future trends and perspectivesDuring this study, the following areas of improvement have been identified: comprehensive understanding of hydraulic fracture network complexity and modelling of stimulated reservoir volume with spatially and temporary variable properties. These are uncertain, but measurable with advanced laboratory and reservoir techniques, e.g. microseismic data integration, modelling of the process of fracturing (i.e. using the discrete fracture network (DFN) approach and geomechanical modelling to represent both the reactivation of natural fractures as well as the creation of new ones). This will minimise interpretation errors, enhance history matching and provide more realistic models to perform stimulation design, production forecasting and reservoir management.

AcknowledgementsThe authors thank the engineers and managers of the PumaFlow™ Reservoir Simulation Group who have assisted in this project, and Beicip-Franlab for permission to publish this paper. Their technical contributions, fruitful discussions, critical remarks and valuable comments are gratefully acknowledged.

DisclaimerThe views expressed in this article are those of the authors and do not necessarily represent those of Beicip-Franlab and IFP Energies Nouvelles.

References1. New Lens Scenarios. A Shift in Perspective for a World in Transition.

Royal Dutch Shell. March, 2013.2. Darishchev, A., Lemouzy, P., Rouvroy, P. 2013. On Simulation of Flow in

Tight and Shale Gas Reservoirs. Paper SPE 163990 presented at the SPE Middle East Unconventional Gas Conference and Exhibition, Muscat, Oman, 28 – 30 Jan. 2013.

3. Mayerhofer M.J., et al. 2006. Integration of Microseismic Fracture Mapping Results With Numerical Fracture Network Production Modeling in Barnett Shale. Paper SPE 102103 presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 24 – 27 Sept. 2006.

4. Blanc, G., et al. 1996. Transient Productivity Index for Numerical Well Test Simulations. Public Document, Institut Français du Pétrole, Pau, France.

5. Todd, M.R., O’Dell, P.M., Hirasaki, G.J. 1972. Methods for Increased Accuracy in Numerical Reservoir Simulators. SPE Transactions Journal, Paper SPE 3516.

Notes* Now at IFP Energies Nouvelles.** Source: www.aterraexploration.com† At least 90% of shale gas wells have SRV of 700x106 ft3/well and over.

Figure 5. Pressure decline in stimulated and unstimulated reservoir volumes.

Figure 6. Cumulative gas production and BHP: reference model (green curve) versus 2Φ-1K model (blue curve), 2Φ-2K (brown curve).